Production systems typically involve significant uncertainty in their operation due to either external or internal sources. The existence of uncertainty transforms conventional deterministic process models to stochastic/parametric problems, the solution of which requires the application of specialized optimization techniques. The main objective of this thesis is to develop suitable algorithms and numerical techniques for the efficient solution of process engineering problems involving uncertain parameters. Based on modelling issues regarding uncertainty classification (deterministic and stochastic uncertain parameters) and design objectives with respect to uncertainty (fixed degree of flexibility and optimal degree of flexibility), a unified multiperiod/stochastic two-stage optimization formulation is proposed and a decomposition based algorithmic procedure is developed for its efficient solution. The proposed algorithm forms the basis for addressing process design problems, planning and scheduling problems and problems related to behavioural analysis under uncertainty. For batch plant design problems involving uncertainty in the description of process parameters such as transfer coefficients, kinetic constants, etc., as well as variability of external parameters such as product demand, economic cost data etc., the exploitation of the special structure coupled with the relaxation of feasibility requirement regarding product demands enables the transformation of the stochastic two-stage programming problems to a single optimization model where the structure of the deterministic problem is fully preserved. For the case of continuous size of equipments, an efficient global optimization procedure is proposed, whereas for the case of discrete equipment sizes the algorithm reduces to the solution of a mixed integer linear programming problem. For short term production planning and long-range planning problems including capacity expansion options, the application of the proposed approach results in the optimal production plan (i. e. process utilization levels, purchases and sales of materials) and/or an optimal capacity expansion policy that maximize an expected profit and ensure an optimal level of future feasibility. Finally, an attempt to address the question of the future "value" of uncertainty is presented based on the concept of value of perfect information. It is shown that the proposed algorithmic developments can be effectively extended to include both the solution of the here-and-now and the wait-and-see models in order to analyze and integrate the